Any closed continuous plane curve can be expressed as an isomorphic transform which relates all points to a unique central description called the symmetric axis. Algorithms have been developed and implemented which permit a digital computer to reversibly transform data derived from cephalometric radiographs into such a description. When applied to the average shape of mandibles extracted from the Broadbent-Bolton series, axis points produce a characteristic shape which appears to be independent of age. Analysis of higher order relationships exhibited by the symmetric axis functions provides quantitative bases for characterizing the curvature of boundaries and segmentation of shape into mathematically tractable elements.